C# - Find SQRT by Guess - Approximation method
You can solve the problem in two ways with out using the built in function System.Math.Sqrt.
Method 1 - Like binary search, have a minimum and maximum possible values. Do the square operation and compare the result. Then adjust minimum or maximum until we find the correct sqrt of the given number. NOTE: This is NOT a perfect square root and it has got accuracy of 4 decimal points. Method 1 is explained on this page.
Method 2 - The traditional way of doing with out calculator or any assumption is using the algorithm. It will be perfect square root up to N number of decimal points meaning the limitation of float and double. Click here to go to algorithmic source code for finding square root.
Source Code
using System;
using System.Collections.Generic;
using System.Text;
namespace SoftwareAndFinance
{
class Math
{
static public double SQRTByGuess(double num)
{
// Assume that the number is less than 1,000,000. so that the maximum of SQRT would be 1000.
// Lets assume the result is 1000. If you want you can increase this limit
double min = 0, max = 1000;
double answer = 0;
double test = 0;
if (num < 0)
{
Console.WriteLine("Negative numbers are not allowed");
return -1;
}
else if (num == 0)
return 0;
while (true)
{
test = (min + max) / 2;
answer = test * test;
if (num > answer)
{
// min needs be moved
min = test;
}
else if (num < answer)
{
// max needs be moved
max = test;
}
if (num == answer)
break;
if (num > (answer - 0.0001) &&
num < (answer + 0.0001))
break;
}
return test;
}
static void Main(string[] args)
{
for (double d = 0; d <= 10000; d += 50)
Console.WriteLine("sqrt({0,6:f1}) = {1,8:f4} {2,8:f4}", d, SQRTByGuess(d), System.Math.Sqrt(d));
}
}
}
Click here to get the C# project along with executable
Output
sqrt( 0.0) = 0.0000 0.0000
sqrt( 50.0) = 7.0711 7.0711
sqrt( 100.0) = 10.0000 10.0000
sqrt( 150.0) = 12.2475 12.2474
sqrt( 200.0) = 14.1421 14.1421
sqrt( 250.0) = 15.8114 15.8114
sqrt( 300.0) = 17.3205 17.3205
sqrt( 350.0) = 18.7083 18.7083
sqrt( 400.0) = 20.0000 20.0000
sqrt( 450.0) = 21.2132 21.2132
sqrt( 500.0) = 22.3607 22.3607
sqrt( 550.0) = 23.4521 23.4521
sqrt( 600.0) = 24.4949 24.4949
sqrt( 650.0) = 25.4951 25.4951
sqrt( 700.0) = 26.4575 26.4575
sqrt( 750.0) = 27.3861 27.3861
sqrt( 800.0) = 28.2843 28.2843
sqrt( 850.0) = 29.1548 29.1548
sqrt( 900.0) = 30.0000 30.0000
sqrt( 950.0) = 30.8221 30.8221
sqrt(1000.0) = 31.6228 31.6228
sqrt(1050.0) = 32.4037 32.4037
sqrt(1100.0) = 33.1662 33.1662
sqrt(1150.0) = 33.9116 33.9116
sqrt(1200.0) = 34.6410 34.6410
sqrt(1250.0) = 35.3553 35.3553
sqrt(1300.0) = 36.0555 36.0555
sqrt(1350.0) = 36.7423 36.7423
sqrt(1400.0) = 37.4166 37.4166
sqrt(1450.0) = 38.0789 38.0789
sqrt(1500.0) = 38.7298 38.7298
sqrt(1550.0) = 39.3700 39.3700
sqrt(1600.0) = 40.0000 40.0000
sqrt(1650.0) = 40.6202 40.6202
sqrt(1700.0) = 41.2311 41.2311
sqrt(1750.0) = 41.8330 41.8330
sqrt(1800.0) = 42.4264 42.4264
sqrt(1850.0) = 43.0116 43.0116
sqrt(1900.0) = 43.5890 43.5890
sqrt(1950.0) = 44.1588 44.1588
sqrt(2000.0) = 44.7214 44.7214
sqrt(2050.0) = 45.2769 45.2769
sqrt(2100.0) = 45.8258 45.8258
sqrt(2150.0) = 46.3681 46.3681
sqrt(2200.0) = 46.9042 46.9042
sqrt(2250.0) = 47.4342 47.4342
sqrt(2300.0) = 47.9583 47.9583
sqrt(2350.0) = 48.4768 48.4768
sqrt(2400.0) = 48.9898 48.9898
sqrt(2450.0) = 49.4975 49.4975
sqrt(2500.0) = 50.0000 50.0000
sqrt(2550.0) = 50.4975 50.4975
sqrt(2600.0) = 50.9902 50.9902
sqrt(2650.0) = 51.4782 51.4782
sqrt(2700.0) = 51.9615 51.9615
sqrt(2750.0) = 52.4404 52.4404
sqrt(2800.0) = 52.9150 52.9150
sqrt(2850.0) = 53.3854 53.3854
sqrt(2900.0) = 53.8516 53.8516
sqrt(2950.0) = 54.3139 54.3139
sqrt(3000.0) = 54.7723 54.7723
sqrt(3050.0) = 55.2268 55.2268
sqrt(3100.0) = 55.6776 55.6776
sqrt(3150.0) = 56.1249 56.1249
sqrt(3200.0) = 56.5685 56.5685
sqrt(3250.0) = 57.0088 57.0088
sqrt(3300.0) = 57.4456 57.4456
sqrt(3350.0) = 57.8792 57.8792
sqrt(3400.0) = 58.3095 58.3095
sqrt(3450.0) = 58.7367 58.7367
sqrt(3500.0) = 59.1608 59.1608
sqrt(3550.0) = 59.5819 59.5819
sqrt(3600.0) = 60.0000 60.0000
sqrt(3650.0) = 60.4152 60.4152
sqrt(3700.0) = 60.8276 60.8276
sqrt(3750.0) = 61.2372 61.2372
sqrt(3800.0) = 61.6441 61.6441
sqrt(3850.0) = 62.0484 62.0484
sqrt(3900.0) = 62.4500 62.4500
sqrt(3950.0) = 62.8490 62.8490
sqrt(4000.0) = 63.2456 63.2456
sqrt(4050.0) = 63.6396 63.6396
sqrt(4100.0) = 64.0312 64.0312
sqrt(4150.0) = 64.4205 64.4205
sqrt(4200.0) = 64.8074 64.8074
sqrt(4250.0) = 65.1920 65.1920
sqrt(4300.0) = 65.5744 65.5744
sqrt(4350.0) = 65.9545 65.9545
sqrt(4400.0) = 66.3325 66.3325
sqrt(4450.0) = 66.7083 66.7083
sqrt(4500.0) = 67.0820 67.0820
sqrt(4550.0) = 67.4537 67.4537
sqrt(4600.0) = 67.8233 67.8233
sqrt(4650.0) = 68.1909 68.1909
sqrt(4700.0) = 68.5565 68.5565
sqrt(4750.0) = 68.9202 68.9202
sqrt(4800.0) = 69.2820 69.2820
sqrt(4850.0) = 69.6419 69.6419
sqrt(4900.0) = 70.0000 70.0000
sqrt(4950.0) = 70.3562 70.3562
sqrt(5000.0) = 70.7107 70.7107
sqrt(5050.0) = 71.0634 71.0634
sqrt(5100.0) = 71.4143 71.4143
sqrt(5150.0) = 71.7635 71.7635
sqrt(5200.0) = 72.1110 72.1110
sqrt(5250.0) = 72.4569 72.4569
sqrt(5300.0) = 72.8011 72.8011
sqrt(5350.0) = 73.1437 73.1437
sqrt(5400.0) = 73.4847 73.4847
sqrt(5450.0) = 73.8241 73.8241
sqrt(5500.0) = 74.1620 74.1620
sqrt(5550.0) = 74.4983 74.4983
sqrt(5600.0) = 74.8331 74.8331
sqrt(5650.0) = 75.1665 75.1665
sqrt(5700.0) = 75.4983 75.4983
sqrt(5750.0) = 75.8288 75.8288
sqrt(5800.0) = 76.1577 76.1577
sqrt(5850.0) = 76.4853 76.4853
sqrt(5900.0) = 76.8115 76.8115
sqrt(5950.0) = 77.1362 77.1362
sqrt(6000.0) = 77.4597 77.4597
sqrt(6050.0) = 77.7817 77.7817
sqrt(6100.0) = 78.1025 78.1025
sqrt(6150.0) = 78.4219 78.4219
sqrt(6200.0) = 78.7401 78.7401
sqrt(6250.0) = 79.0569 79.0569
sqrt(6300.0) = 79.3725 79.3725
sqrt(6350.0) = 79.6869 79.6869
sqrt(6400.0) = 80.0000 80.0000
sqrt(6450.0) = 80.3119 80.3119
sqrt(6500.0) = 80.6226 80.6226
sqrt(6550.0) = 80.9321 80.9321
sqrt(6600.0) = 81.2404 81.2404
sqrt(6650.0) = 81.5475 81.5475
sqrt(6700.0) = 81.8535 81.8535
sqrt(6750.0) = 82.1584 82.1584
sqrt(6800.0) = 82.4621 82.4621
sqrt(6850.0) = 82.7647 82.7647
sqrt(6900.0) = 83.0662 83.0662
sqrt(6950.0) = 83.3667 83.3667
sqrt(7000.0) = 83.6660 83.6660
sqrt(7050.0) = 83.9643 83.9643
sqrt(7100.0) = 84.2615 84.2615
sqrt(7150.0) = 84.5577 84.5577
sqrt(7200.0) = 84.8528 84.8528
sqrt(7250.0) = 85.1469 85.1469
sqrt(7300.0) = 85.4400 85.4400
sqrt(7350.0) = 85.7321 85.7321
sqrt(7400.0) = 86.0233 86.0233
sqrt(7450.0) = 86.3134 86.3134
sqrt(7500.0) = 86.6025 86.6025
sqrt(7550.0) = 86.8907 86.8907
sqrt(7600.0) = 87.1780 87.1780
sqrt(7650.0) = 87.4643 87.4643
sqrt(7700.0) = 87.7496 87.7496
sqrt(7750.0) = 88.0341 88.0341
sqrt(7800.0) = 88.3176 88.3176
sqrt(7850.0) = 88.6002 88.6002
sqrt(7900.0) = 88.8819 88.8819
sqrt(7950.0) = 89.1628 89.1628
sqrt(8000.0) = 89.4427 89.4427
sqrt(8050.0) = 89.7218 89.7218
sqrt(8100.0) = 90.0000 90.0000
sqrt(8150.0) = 90.2774 90.2774
sqrt(8200.0) = 90.5539 90.5539
sqrt(8250.0) = 90.8295 90.8295
sqrt(8300.0) = 91.1043 91.1043
sqrt(8350.0) = 91.3783 91.3783
sqrt(8400.0) = 91.6515 91.6515
sqrt(8450.0) = 91.9239 91.9239
sqrt(8500.0) = 92.1954 92.1954
sqrt(8550.0) = 92.4662 92.4662
sqrt(8600.0) = 92.7362 92.7362
sqrt(8650.0) = 93.0054 93.0054
sqrt(8700.0) = 93.2738 93.2738
sqrt(8750.0) = 93.5414 93.5414
sqrt(8800.0) = 93.8083 93.8083
sqrt(8850.0) = 94.0744 94.0744
sqrt(8900.0) = 94.3398 94.3398
sqrt(8950.0) = 94.6044 94.6044
sqrt(9000.0) = 94.8683 94.8683
sqrt(9050.0) = 95.1315 95.1315
sqrt(9100.0) = 95.3939 95.3939
sqrt(9150.0) = 95.6556 95.6556
sqrt(9200.0) = 95.9166 95.9166
sqrt(9250.0) = 96.1769 96.1769
sqrt(9300.0) = 96.4365 96.4365
sqrt(9350.0) = 96.6954 96.6954
sqrt(9400.0) = 96.9536 96.9536
sqrt(9450.0) = 97.2111 97.2111
sqrt(9500.0) = 97.4679 97.4679
sqrt(9550.0) = 97.7241 97.7241
sqrt(9600.0) = 97.9796 97.9796
sqrt(9650.0) = 98.2344 98.2344
sqrt(9700.0) = 98.4886 98.4886
sqrt(9750.0) = 98.7421 98.7421
sqrt(9800.0) = 98.9949 98.9949
sqrt(9850.0) = 99.2472 99.2472
sqrt(9900.0) = 99.4987 99.4987
sqrt(9950.0) = 99.7497 99.7497
sqrt(10000.0) = 100.0000 100.0000
Press any key to continue . . .
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